alpar@906: /* -*- C++ -*-
ladanyi@1435:  * lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library
alpar@906:  *
alpar@1875:  * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@906:  *
alpar@906:  * Permission to use, modify and distribute this software is granted
alpar@906:  * provided that this copyright notice appears in all copies. For
alpar@906:  * precise terms see the accompanying LICENSE file.
alpar@906:  *
alpar@906:  * This software is provided "AS IS" with no warranty of any kind,
alpar@906:  * express or implied, and with no claim as to its suitability for any
alpar@906:  * purpose.
alpar@906:  *
alpar@906:  */
alpar@255: 
alpar@921: #ifndef LEMON_FIB_HEAP_H
alpar@921: #define LEMON_FIB_HEAP_H
alpar@255: 
jacint@857: ///\file
klao@491: ///\ingroup auxdat
alpar@255: ///\brief Fibonacci Heap implementation.
alpar@255: 
alpar@255: #include <vector>
alpar@255: #include <functional>
deba@1332: #include <cmath>
alpar@255: 
alpar@921: namespace lemon {
alpar@255:   
deba@1834:   /// \ingroup auxdat
alpar@430: 
jacint@857:   /// Fibonacci Heap.
jacint@373: 
jacint@857:   ///This class implements the \e Fibonacci \e heap data structure. A \e heap
jacint@857:   ///is a data structure for storing items with specified values called \e
jacint@857:   ///priorities in such a way that finding the item with minimum priority is
alpar@911:   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
jacint@857:   ///one can change the priority of an item, add or erase an item, etc.
jacint@857:   ///
jacint@857:   ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
jacint@857:   ///heap. In case of many calls to these operations, it is better to use a
jacint@857:   ///\e binary \e heap.
jacint@857:   ///
jacint@857:   ///\param Item Type of the items to be stored.  
jacint@857:   ///\param Prio Type of the priority of the items.
alpar@1204:   ///\param ItemIntMap A read and writable Item int map, used internally
alpar@1204:   ///to handle the cross references.
jacint@857:   ///\param Compare A class for the ordering of the priorities. The
jacint@857:   ///default is \c std::less<Prio>.
jacint@857:   ///
alpar@967:   ///\sa BinHeap
alpar@967:   ///\sa Dijkstra
jacint@857:   ///\author Jacint Szabo 
jacint@857:  
jacint@373: #ifdef DOXYGEN
jacint@373:   template <typename Item, 
jacint@373: 	    typename Prio, 
jacint@373: 	    typename ItemIntMap, 
jacint@373: 	    typename Compare>
jacint@373: #else
jacint@373:   template <typename Item, 
jacint@373: 	    typename Prio, 
jacint@373: 	    typename ItemIntMap, 
alpar@255: 	    typename Compare = std::less<Prio> >
jacint@373: #endif
alpar@255:   class FibHeap {
jacint@387:   public:     
alpar@255:     typedef Prio PrioType;
alpar@255:     
jacint@373:   private:
alpar@255:     class store;
alpar@255:     
alpar@255:     std::vector<store> container;
alpar@255:     int minimum;
alpar@255:     ItemIntMap &iimap;
alpar@255:     Compare comp;
alpar@255:     int num_items;
jacint@373:     
alpar@255:   public:
alpar@1127:     ///Status of the nodes
alpar@255:     enum state_enum {
alpar@1127:       ///The node is in the heap
alpar@255:       IN_HEAP = 0,
alpar@1127:       ///The node has never been in the heap
alpar@255:       PRE_HEAP = -1,
alpar@1127:       ///The node was in the heap but it got out of it
alpar@255:       POST_HEAP = -2
alpar@255:     };
alpar@255:     
deba@1717:     /// \brief The constructor
deba@1717:     ///
deba@1717:     /// \c _iimap should be given to the constructor, since it is
deba@1717:     ///   used internally to handle the cross references.
deba@1185:     explicit FibHeap(ItemIntMap &_iimap) 
deba@1185:       : minimum(0), iimap(_iimap), num_items() {} 
jacint@1270:  
deba@1717:     /// \brief The constructor
deba@1717:     ///
deba@1717:     /// \c _iimap should be given to the constructor, since it is used
deba@1717:     /// internally to handle the cross references. \c _comp is an
deba@1717:     /// object for ordering of the priorities. 
jacint@373:     FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), 
jacint@1270: 		  iimap(_iimap), comp(_comp), num_items() {}
alpar@255:     
deba@1717:     /// \brief The number of items stored in the heap.
deba@1717:     ///
deba@1717:     /// Returns the number of items stored in the heap.
jacint@373:     int size() const { return num_items; }
jacint@373: 
deba@1717:     /// \brief Checks if the heap stores no items.
deba@1717:     ///
deba@1717:     ///   Returns \c true if and only if the heap stores no items.
jacint@373:     bool empty() const { return num_items==0; }
jacint@373: 
deba@1717:     /// \brief Make empty this heap.
deba@1717:     /// 
deba@1717:     /// Make empty this heap.
deba@1753:     void clear() {
deba@1753:       if (num_items != 0) {
deba@1753: 	for (int i = 0; i < (int)container.size(); ++i) {
deba@1753: 	  iimap[container[i].name] = -2;
deba@1753: 	}
deba@1717:       }
deba@1717:       container.clear(); minimum = 0; num_items = 0;
deba@1717:     }
jacint@373: 
deba@1717:     /// \brief \c item gets to the heap with priority \c value independently 
deba@1717:     /// if \c item was already there.
deba@1717:     ///
deba@1717:     /// This method calls \ref push(\c item, \c value) if \c item is not
deba@1717:     /// stored in the heap and it calls \ref decrease(\c item, \c value) or
deba@1717:     /// \ref increase(\c item, \c value) otherwise.
jacint@387:     void set (Item const item, PrioType const value); 
jacint@373:     
deba@1717:     /// \brief Adds \c item to the heap with priority \c value. 
deba@1717:     ///    
deba@1717:     /// Adds \c item to the heap with priority \c value. 
deba@1717:     /// \pre \c item must not be stored in the heap. 
jacint@387:     void push (Item const item, PrioType const value);
jacint@373:     
deba@1717:     /// \brief Returns the item with minimum priority relative to \c Compare.
deba@1717:     ///
deba@1717:     /// This method returns the item with minimum priority relative to \c
deba@1717:     /// Compare.  
deba@1717:     /// \pre The heap must be nonempty.  
jacint@373:     Item top() const { return container[minimum].name; }
jacint@373: 
deba@1717:     /// \brief Returns the minimum priority relative to \c Compare.
deba@1717:     ///
deba@1717:     /// It returns the minimum priority relative to \c Compare.
deba@1717:     /// \pre The heap must be nonempty.
jacint@373:     PrioType prio() const { return container[minimum].prio; }
jacint@373:     
deba@1717:     /// \brief Returns the priority of \c item.
deba@1717:     ///
deba@1717:     /// This function returns the priority of \c item.
deba@1717:     /// \pre \c item must be in the heap.
jacint@387:     PrioType& operator[](const Item& item) { 
jacint@387:       return container[iimap[item]].prio; 
jacint@387:     }
jacint@373:     
deba@1717:     /// \brief Returns the priority of \c item.
deba@1717:     ///
deba@1717:     /// It returns the priority of \c item.
deba@1717:     /// \pre \c item must be in the heap.
jacint@387:     const PrioType& operator[](const Item& item) const { 
jacint@387:       return container[iimap[item]].prio; 
alpar@255:     }
alpar@255: 
alpar@255: 
deba@1717:     /// \brief Deletes the item with minimum priority relative to \c Compare.
deba@1717:     ///
deba@1717:     /// This method deletes the item with minimum priority relative to \c
deba@1717:     /// Compare from the heap.  
deba@1717:     /// \pre The heap must be non-empty.  
jacint@373:     void pop();
jacint@373: 
deba@1717:     /// \brief Deletes \c item from the heap.
deba@1717:     ///
deba@1717:     /// This method deletes \c item from the heap, if \c item was already
deba@1717:     /// stored in the heap. It is quite inefficient in Fibonacci heaps.
jacint@387:     void erase (const Item& item); 
jacint@373: 
deba@1717:     /// \brief Decreases the priority of \c item to \c value.
deba@1717:     ///
deba@1717:     /// This method decreases the priority of \c item to \c value.
deba@1717:     /// \pre \c item must be stored in the heap with priority at least \c
deba@1717:     ///   value relative to \c Compare.
jacint@387:     void decrease (Item item, PrioType const value); 
jacint@373: 
deba@1717:     /// \brief Increases the priority of \c item to \c value.
deba@1717:     ///
deba@1717:     /// This method sets the priority of \c item to \c value. Though
deba@1717:     /// there is no precondition on the priority of \c item, this
deba@1717:     /// method should be used only if it is indeed necessary to increase
deba@1717:     /// (relative to \c Compare) the priority of \c item, because this
deba@1717:     /// method is inefficient.
jacint@387:     void increase (Item item, PrioType const value) {
jacint@387:       erase(item);
jacint@387:       push(item, value);
jacint@373:     }
jacint@373: 
jacint@373: 
deba@1717:     /// \brief Returns if \c item is in, has already been in, or has never 
deba@1717:     /// been in the heap.
deba@1717:     ///
deba@1717:     /// This method returns PRE_HEAP if \c item has never been in the
deba@1717:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
deba@1717:     /// otherwise. In the latter case it is possible that \c item will
deba@1717:     /// get back to the heap again.
jacint@387:     state_enum state(const Item &item) const {
jacint@387:       int i=iimap[item];
jacint@387:       if( i>=0 ) {
jacint@387: 	if ( container[i].in ) i=0;
jacint@387: 	else i=-2; 
jacint@387:       }
jacint@387:       return state_enum(i);
jacint@387:     }    
deba@1902: 
deba@1902:     /// \brief Sets the state of the \c item in the heap.
deba@1902:     ///
deba@1902:     /// Sets the state of the \c item in the heap. It can be used to
deba@1902:     /// manually clear the heap when it is important to achive the
deba@1902:     /// better time complexity.
deba@1902:     /// \param i The item.
deba@1902:     /// \param st The state. It should not be \c IN_HEAP. 
deba@1902:     void state(const Item& i, state_enum st) {
deba@1902:       switch (st) {
deba@1902:       case POST_HEAP:
deba@1902:       case PRE_HEAP:
deba@1902:         if (state(i) == IN_HEAP) {
deba@1902:           erase(i);
deba@1902:         }
deba@1903:         iimap[i] = st;
deba@1902:         break;
deba@1906:       case IN_HEAP:
deba@1906:         break;
deba@1902:       }
deba@1902:     }
jacint@387:     
jacint@387:   private:
jacint@387:     
jacint@387:     void balance();
jacint@387:     void makeroot(int c);
jacint@387:     void cut(int a, int b);
jacint@387:     void cascade(int a);
jacint@387:     void fuse(int a, int b);
jacint@387:     void unlace(int a);
jacint@373: 
jacint@373: 
jacint@387:     class store {
jacint@387:       friend class FibHeap;
jacint@387:       
jacint@387:       Item name;
jacint@387:       int parent;
jacint@387:       int left_neighbor;
jacint@387:       int right_neighbor;
jacint@387:       int child;
jacint@387:       int degree;  
jacint@387:       bool marked;
jacint@387:       bool in;
jacint@387:       PrioType prio;
jacint@387:       
jacint@387:       store() : parent(-1), child(-1), degree(), marked(false), in(true) {} 
jacint@387:     };
jacint@387:   };    
jacint@387:  
jacint@387: 
jacint@373: 
jacint@373:     // **********************************************************************
jacint@373:     //  IMPLEMENTATIONS
jacint@373:     // **********************************************************************
jacint@373:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::set 
jacint@387:   (Item const item, PrioType const value) 
jacint@387:   {
jacint@387:     int i=iimap[item];
jacint@387:     if ( i >= 0 && container[i].in ) {
jacint@387:       if ( comp(value, container[i].prio) ) decrease(item, value); 
jacint@387:       if ( comp(container[i].prio, value) ) increase(item, value); 
jacint@387:     } else push(item, value);
jacint@387:   }
alpar@255:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::push 
jacint@387:   (Item const item, PrioType const value) {
jacint@387:       int i=iimap[item];      
alpar@255:       if ( i < 0 ) {
alpar@255: 	int s=container.size();
jacint@387: 	iimap.set( item, s );	
alpar@255: 	store st;
jacint@387: 	st.name=item;
alpar@255: 	container.push_back(st);
alpar@255: 	i=s;
alpar@255:       } else {
alpar@255: 	container[i].parent=container[i].child=-1;
alpar@255: 	container[i].degree=0;
alpar@255: 	container[i].in=true;
alpar@255: 	container[i].marked=false;
alpar@255:       }
alpar@255: 
alpar@255:       if ( num_items ) {
alpar@255: 	container[container[minimum].right_neighbor].left_neighbor=i;
alpar@255: 	container[i].right_neighbor=container[minimum].right_neighbor;
alpar@255: 	container[minimum].right_neighbor=i;
alpar@255: 	container[i].left_neighbor=minimum;
alpar@255: 	if ( comp( value, container[minimum].prio) ) minimum=i; 
alpar@255:       } else {
alpar@255: 	container[i].right_neighbor=container[i].left_neighbor=i;
alpar@255: 	minimum=i;	
alpar@255:       }
alpar@255:       container[i].prio=value;
alpar@255:       ++num_items;
alpar@255:     }
alpar@255:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
alpar@255:       /*The first case is that there are only one root.*/
alpar@255:       if ( container[minimum].left_neighbor==minimum ) {
alpar@255: 	container[minimum].in=false;
alpar@255: 	if ( container[minimum].degree!=0 ) { 
alpar@255: 	  makeroot(container[minimum].child);
alpar@255: 	  minimum=container[minimum].child;
alpar@255: 	  balance();
alpar@255: 	}
alpar@255:       } else {
alpar@255: 	int right=container[minimum].right_neighbor;
alpar@255: 	unlace(minimum);
alpar@255: 	container[minimum].in=false;
alpar@255: 	if ( container[minimum].degree > 0 ) {
alpar@255: 	  int left=container[minimum].left_neighbor;
alpar@255: 	  int child=container[minimum].child;
alpar@255: 	  int last_child=container[child].left_neighbor;
alpar@255: 	
alpar@255: 	  makeroot(child);
alpar@255: 	  
alpar@255: 	  container[left].right_neighbor=child;
alpar@255: 	  container[child].left_neighbor=left;
alpar@255: 	  container[right].left_neighbor=last_child;
alpar@255: 	  container[last_child].right_neighbor=right;
alpar@255: 	}
alpar@255: 	minimum=right;
alpar@255: 	balance();
alpar@255:       } // the case where there are more roots
alpar@255:       --num_items;   
alpar@255:     }
alpar@255: 
jacint@387: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::erase 
jacint@387:   (const Item& item) {
jacint@387:       int i=iimap[item];
alpar@255:       
alpar@255:       if ( i >= 0 && container[i].in ) { 	
alpar@255: 	if ( container[i].parent!=-1 ) {
alpar@255: 	  int p=container[i].parent;
alpar@255: 	  cut(i,p);	    
alpar@255: 	  cascade(p);
alpar@255: 	}
alpar@255: 	minimum=i;     //As if its prio would be -infinity
alpar@255: 	pop();
alpar@255:       }
jacint@387:   }
alpar@255:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease 
jacint@387:   (Item item, PrioType const value) {
jacint@387:       int i=iimap[item];
alpar@255:       container[i].prio=value;
alpar@255:       int p=container[i].parent;
alpar@255:       
alpar@255:       if ( p!=-1 && comp(value, container[p].prio) ) {
alpar@255: 	cut(i,p);	    
alpar@255: 	cascade(p);
alpar@255:       }      
alpar@255:       if ( comp(value, container[minimum].prio) ) minimum=i; 
jacint@387:   }
jacint@387:  
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {      
alpar@255: 
deba@1332:     int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
alpar@255:   
alpar@255:     std::vector<int> A(maxdeg,-1); 
alpar@255:     
alpar@255:     /*
alpar@255:      *Recall that now minimum does not point to the minimum prio element.
alpar@255:      *We set minimum to this during balance().
alpar@255:      */
alpar@255:     int anchor=container[minimum].left_neighbor; 
alpar@255:     int next=minimum; 
alpar@255:     bool end=false; 
alpar@255:     	
alpar@255:        do {
alpar@255: 	int active=next;
alpar@255: 	if ( anchor==active ) end=true;
alpar@255: 	int d=container[active].degree;
alpar@255: 	next=container[active].right_neighbor;
alpar@255: 
alpar@255: 	while (A[d]!=-1) {	  
alpar@255: 	  if( comp(container[active].prio, container[A[d]].prio) ) {
alpar@255: 	    fuse(active,A[d]); 
alpar@255: 	  } else { 
alpar@255: 	    fuse(A[d],active);
alpar@255: 	    active=A[d];
alpar@255: 	  } 
alpar@255: 	  A[d]=-1;
alpar@255: 	  ++d;
alpar@255: 	}	
alpar@255: 	A[d]=active;
alpar@255:        } while ( !end );
alpar@255: 
alpar@255: 
alpar@255:        while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
alpar@255:        int s=minimum;
alpar@255:        int m=minimum;
alpar@255:        do {  
alpar@255: 	 if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
alpar@255: 	 s=container[s].right_neighbor;
alpar@255:        } while ( s != m );
alpar@255:     }
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot 
jacint@387:   (int c) {
alpar@255:       int s=c;
alpar@255:       do {  
alpar@255: 	container[s].parent=-1;
alpar@255: 	s=container[s].right_neighbor;
alpar@255:       } while ( s != c );
alpar@255:     }
jacint@387:   
jacint@387:   
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::cut 
jacint@387:   (int a, int b) {    
jacint@387:     /*
jacint@387:      *Replacing a from the children of b.
jacint@387:      */
jacint@387:     --container[b].degree;
alpar@255:     
jacint@387:     if ( container[b].degree !=0 ) {
jacint@387:       int child=container[b].child;
jacint@387:       if ( child==a ) 
jacint@387: 	container[b].child=container[child].right_neighbor;
jacint@387:       unlace(a);
jacint@387:     }
jacint@387:     
jacint@387:     
jacint@387:     /*Lacing a to the roots.*/
jacint@387:     int right=container[minimum].right_neighbor;
jacint@387:     container[minimum].right_neighbor=a;
jacint@387:     container[a].left_neighbor=minimum;
jacint@387:     container[a].right_neighbor=right;
jacint@387:     container[right].left_neighbor=a;
jacint@387:     
jacint@387:     container[a].parent=-1;
jacint@387:     container[a].marked=false;
jacint@387:   }
jacint@387:   
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade 
jacint@387:   (int a) 
alpar@255:     {
alpar@255:       if ( container[a].parent!=-1 ) {
alpar@255: 	int p=container[a].parent;
alpar@255: 	
alpar@255: 	if ( container[a].marked==false ) container[a].marked=true;
alpar@255: 	else {
alpar@255: 	  cut(a,p);
alpar@255: 	  cascade(p);
alpar@255: 	}
alpar@255:       }
alpar@255:     }
alpar@255: 
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse 
jacint@387:   (int a, int b) {
alpar@255:       unlace(b);
alpar@255:       
alpar@255:       /*Lacing b under a.*/
alpar@255:       container[b].parent=a;
alpar@255: 
alpar@255:       if (container[a].degree==0) {
alpar@255: 	container[b].left_neighbor=b;
alpar@255: 	container[b].right_neighbor=b;
alpar@255: 	container[a].child=b;	
alpar@255:       } else {
alpar@255: 	int child=container[a].child;
alpar@255: 	int last_child=container[child].left_neighbor;
alpar@255: 	container[child].left_neighbor=b;
alpar@255: 	container[b].right_neighbor=child;
alpar@255: 	container[last_child].right_neighbor=b;
alpar@255: 	container[b].left_neighbor=last_child;
alpar@255:       }
alpar@255: 
alpar@255:       ++container[a].degree;
alpar@255:       
alpar@255:       container[b].marked=false;
alpar@255:     }
alpar@255: 
jacint@387:   
jacint@387:   /*
jacint@387:    *It is invoked only if a has siblings.
jacint@387:    */
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace 
jacint@387:   (int a) {      
alpar@255:       int leftn=container[a].left_neighbor;
alpar@255:       int rightn=container[a].right_neighbor;
alpar@255:       container[leftn].right_neighbor=rightn;
alpar@255:       container[rightn].left_neighbor=leftn;
jacint@387:   }
alpar@255:   
alpar@430: 
alpar@921: } //namespace lemon
alpar@477: 
alpar@921: #endif //LEMON_FIB_HEAP_H
alpar@477: